Click here to close now.


Agile Computing Authors: Yeshim Deniz, Janakiram MSV, Jason Bloomberg, Jayaram Krishnaswamy, Joe Pruitt

Related Topics: Agile Computing

Agile Computing: Article

How Can Metcalfe's Law Be Updated for Web 2.0?

Metcalfe's Law is More Misunderstood Than Wrong

"Metcalfe's Law is Wrong," contended Bob Briscoe, Andrew Odlyzko, and Benjamin Tilly recently in a much-discussed IEEE Spectrum article, in which they wrote: "Of all the popular ideas of the Internet boom, one of the most dangerously influential was Metcalfe's Law." Sim Simeonov disagrees.

The industry is at it again – trying to figure out what to make of Metcalfe’s Law. This time it’s IEEE Spectrum with a controversially titled “Metcalfe’s Law is Wrong”. The main thrust of the argument is that the value of a network grows O(nlogn) as opposed to O(n2). Unfortunately, the authors’ O(nlogn) suggestion is no more accurate or insightful than the original proposal.

There are three issues to consider:

  • The difference between what Bob Metcalfe claimed and what ended up becoming Metcalfe’s Law
  • The units of measurement
  • What happens with large networks

The typical statement of the law is “the value of a network increases proportionately with the square of the number of its users.” That’s what you’ll find at the Wikipedia link above. It happens to not be what Bob Metcalfe claimed in the first place. These days I work with Bob at Polaris Venture Partners. I have seen a copy of the original (circa 1980) transparency that Bob created to communicate his idea. IEEE Spectrum has a good reproduction, shown here.

The original Metcalfe's Law graph

The unit of measurement along the X-axis is “compatibly communicating devices”, not users. The credit for the “users” formulation goes to George Gilder who wrote about Metcalfe’s Law in Forbes ASAP on September 13, 1993. However, Gilder’s article talks about machines and not users. Anyway, both the “users” and “machines” formulations miss the subtlety imposed by the “compatibly communicating” qualifier, which is the key to understanding the concept.

Bob, who invented Ethernet, was addressing small LANs where machines are visible to one another and share services such as discovery, email, etc. He recalls that his goal was to have companies install networks with at least three nodes. Now, that’s a far cry from the Internet, which is huge, where most machines cannot see one another and/or have nothing to communicate about… So, if you’re talking about a smallish network where indeed nodes are “compatibly communicating”, I’d argue that the original suggestion holds pretty well.

The authors of the IEEE article take the “users” formulation and suggest that the value of a network should grow on the order of O(nlogn) as opposed to O(n2). Are they correct? It depends. Is their proposal a meaningful improvement on the original idea? No.

To justify the logn factor, the authors apply Zipf’s Law to large networks. Again, the issue I have is with the unit of measurement. Zipf’s Law applies to homogeneous populations (the original research was on natural language). You can apply it to books, movies and songs. It’s meaningless to apply it to the population of books, movies and songs put together or, for that matter, to the Internet, which is perhaps the most heterogeneous collection of nodes, people, communities, interests, etc. one can point to. For the same reason, you cannot apply it to MySpace, which is a group of sub-communities hosted on the same online community infrastructure (OCI), or to the Cingular / AT&T Wireless merger.

The main point of Metcalfe’s Law is that the value of networks exhibits super-linear growth. If you measure the size of networks in users, the value definitely does not grow O(n2) but I’m not sure O(nlogn) is a significantly better approximation, especially for large networks. A better approximation of value would be something along the lines of O(SumC(O(mclogmc))), where C is the set of homogeneous sub-networks/communities and mc is the size of the particular sub-community/network. Since the same user can be a member of multiple social networks, and since |C| is a function of N (there are more communities in larger networks), it’s not clear what the total value will end up being. That’s a Long Tail argument if you want one…

Very large networks pose a further problem. Size introduces friction and complicates connectivity, discovery, identity management, trust provisioning, etc. Does this mean that at some point the value of a network starts going down (as another good illustration from the IEEE article shows)? It depends on infrastructure. Clients and servers play different roles in networks. (For more on this in the context of Metcalfe’s Law, see Integration is the Killer App, an article I wrote for XML Journal in 2003, having spent less time thinking about the problem ;-) ). P2P sharing, search engines and portals, anti-spam tools and federated identity management schemes are just but a few examples of the myriad of technologies that have all come about to address scaling problems on the Internet. MySpace and LinkedIn have very different rules of engagement and policing schemes. These communities will grow and increase in value very differently. That’s another argument for the value of a network aggregating across a myriad of sub-networks.

Bottom line, the article attacks Metcalfe’s Law but fails to propose a meaningful alternative.

More Stories By Simeon Simeonov

Simeon Simeonov is CEO of FastIgnite, where he invests in and advises startups. He was chief architect or CTO at companies such as Allaire, Macromedia, Better Advertising and Thing Labs. He blogs at, tweets as @simeons and lives in the Greater Boston area with his wife, son and an adopted dog named Tye.

Comments (6) View Comments

Share your thoughts on this story.

Add your comment
You must be signed in to add a comment. Sign-in | Register

In accordance with our Comment Policy, we encourage comments that are on topic, relevant and to-the-point. We will remove comments that include profanity, personal attacks, racial slurs, threats of violence, or other inappropriate material that violates our Terms and Conditions, and will block users who make repeated violations. We ask all readers to expect diversity of opinion and to treat one another with dignity and respect.

Most Recent Comments
wsanders 08/13/06 08:41:43 AM EDT

I sort of see the key insight of Briscoe, Odlyzko, and Tilly that, if you are going to pull a function out of your ass, it makes more sense if the differential of the function flattens out rather than slopes linearly upwards forever, because there is ultimately a decreasing value of each connection as the number of connections increases.

So they were correct to pull a log function of of their ass, but they could have just as easily pulled out n*ln(n) or some other base. They made no attempt to "calibrate" the model.

A good insight is this quotation:

"If Metcalfe's Law were true, it would create overwhelming incentives for all networks relying on the same technology to merge, or at least to interconnect. These incentives would make isolated networks hard to explain. Consider two networks, each with n members. By Metcalfe's Law, each one's value is on the order of n 2, so the total value of both of these separate networks is roughly 2n 2. But suppose these two networks merge. Then we will effectively have a single network with 2n members, which, by Metcalfe's Law, will be worth (2n)2 or 4n 2--twice as much as the combined value of the two separate networks.

Surely it would require a singularly obtuse management, to say nothing of stunningly inefficient financial markets, to fail to seize this obvious opportunity to double total network value by simply combining the two."

Inflating these "synergies" was exactly what led to the Bombing Off of the Bubble.

MountainLogic 08/13/06 08:38:03 AM EDT

This all came about because Metcalfe was trying to make a case for networking (e.g., ethernet).

Back then the ethernet cards he was selling were expensive. The decision maker would go, "gee, if it cost $x to network two people why can't Bob just walk down the hall to Jan's office?" If X is greater then the cost of Bob "walking down the hall" (or snail mailing or flying...) then there is no busines case for installing a network. More to the point:
If the node cost, x, is $100 and there are 100 users, n, then the cost for the network is $10,000.

If the single user business value, v, of the network is $10 for one user then the ROI for different valuation methods is:

Linear: vn = $1,000 -- no business case, don't even think about it

Metcalf's Law: (n(n-1)=2)v = 49,500 -- winner

Metcalf's Law as misused by dot-bombers: N^2 * V = 100,000 -- "Proves" selling frozen mud on the net is a winner

As restated by the authors: n long (n) * v = 2000 -- no business case, but better than a flat linear

There really are two problems here. The scaling formula and setting the business value. If you set the business value for a single connection greater than the cost of the network then it is a no brainer, but back when Metcalfe was pushing networking that was a hard case to make.

Scott Allen 08/13/06 08:20:00 AM EDT

Metcalfe's Law has always been understood to mean "the theoretical potential value", since a very large number of the links between nodes will never be made.

This same idea can be applied to Reed's Law, which states that the potential value of social networks, i.e., those with self-organizing groups, grows as 2^N (actually, 2^N - N - 1). In reality, of course, this never even comes close, because real groups don't usually organize like that ("let's make a sub-group within our group that excludes one person", etc.).

Also, virtual groups, in particular, don't tend to break off into ad hoc sub-groups if they don't have the tools to do so, e.g., the participants in one thread don't typically say "Let's go create a new group to discuss this." It's theoretically possible, but only occasionally occurs. Of course, the participants in a particular thread can be considered a sort of ad hoc sub-group, in which case you might achieve something closer to the potential, but still...

Interesting stuff - thanks for the link.

Jon Rubin 08/13/06 08:05:56 AM EDT

Metcalfe's Law said that the value of a network, x, as it increases in network members, n, is described by the equation x=n^2.

In other words, it said the value of a network was proportional to the square of the network's users.

Instead, the IEEE article declares it should be x=n"log(n). My suspicion - and this has no basis in anything and I haven't even graphed it and my total knowledge of information theory is that it was started by a guy named Claude - is that Euler has to be involved somewhere and maybe x=n"ln(n) would be more correct.

Peter O'Kelly 08/13/06 08:03:17 AM EDT

insightful analysis

Johannes Ernst 08/13/06 07:58:19 AM EDT

Of course Metcalfe's Law is overstated! If I have a fax machine and somebody in central China, who I have never heard of and will never interact with, buys another fax machine, the value of the network will not grow proportionally to N (say, hundreds of millions: the number of fax machines in existence today) but by some much smaller number such as a couple of hundred at the maximum (the number of fax machines that person will ever send a fax to or receive a fax from)...

@ThingsExpo Stories
Electric power utilities face relentless pressure on their financial performance, and reducing distribution grid losses is one of the last untapped opportunities to meet their business goals. Combining IoT-enabled sensors and cloud-based data analytics, utilities now are able to find, quantify and reduce losses faster – and with a smaller IT footprint. Solutions exist using Internet-enabled sensors deployed temporarily at strategic locations within the distribution grid to measure actual line loads.
The Internet of Everything is re-shaping technology trends–moving away from “request/response” architecture to an “always-on” Streaming Web where data is in constant motion and secure, reliable communication is an absolute necessity. As more and more THINGS go online, the challenges that developers will need to address will only increase exponentially. In his session at @ThingsExpo, Todd Greene, Founder & CEO of PubNub, will explore the current state of IoT connectivity and review key trends and technology requirements that will drive the Internet of Things from hype to reality.
SYS-CON Events announced today that IBM Cloud Data Services has been named “Bronze Sponsor” of SYS-CON's 17th Cloud Expo, which will take place on November 3–5, 2015, at the Santa Clara Convention Center in Santa Clara, CA. IBM Cloud Data Services offers a portfolio of integrated, best-of-breed cloud data services for developers focused on mobile computing and analytics use cases.
The Internet of Things (IoT) is growing rapidly by extending current technologies, products and networks. By 2020, Cisco estimates there will be 50 billion connected devices. Gartner has forecast revenues of over $300 billion, just to IoT suppliers. Now is the time to figure out how you’ll make money – not just create innovative products. With hundreds of new products and companies jumping into the IoT fray every month, there’s no shortage of innovation. Despite this, McKinsey/VisionMobile data shows "less than 10 percent of IoT developers are making enough to support a reasonably sized team....
Today air travel is a minefield of delays, hassles and customer disappointment. Airlines struggle to revitalize the experience. GE and M2Mi will demonstrate practical examples of how IoT solutions are helping airlines bring back personalization, reduce trip time and improve reliability. In their session at @ThingsExpo, Shyam Varan Nath, Principal Architect with GE, and Dr. Sarah Cooper, M2Mi's VP Business Development and Engineering, will explore the IoT cloud-based platform technologies driving this change including privacy controls, data transparency and integration of real time context w...
Developing software for the Internet of Things (IoT) comes with its own set of challenges. Security, privacy, and unified standards are a few key issues. In addition, each IoT product is comprised of at least three separate application components: the software embedded in the device, the backend big-data service, and the mobile application for the end user's controls. Each component is developed by a different team, using different technologies and practices, and deployed to a different stack/target - this makes the integration of these separate pipelines and the coordination of software upd...
As a company adopts a DevOps approach to software development, what are key things that both the Dev and Ops side of the business must keep in mind to ensure effective continuous delivery? In his session at DevOps Summit, Mark Hydar, Head of DevOps, Ericsson TV Platforms, will share best practices and provide helpful tips for Ops teams to adopt an open line of communication with the development side of the house to ensure success between the two sides.
There will be 20 billion IoT devices connected to the Internet soon. What if we could control these devices with our voice, mind, or gestures? What if we could teach these devices how to talk to each other? What if these devices could learn how to interact with us (and each other) to make our lives better? What if Jarvis was real? How can I gain these super powers? In his session at 17th Cloud Expo, Chris Matthieu, co-founder and CTO of Octoblu, will show you!
Mobile messaging has been a popular communication channel for more than 20 years. Finnish engineer Matti Makkonen invented the idea for SMS (Short Message Service) in 1984, making his vision a reality on December 3, 1992 by sending the first message ("Happy Christmas") from a PC to a cell phone. Since then, the technology has evolved immensely, from both a technology standpoint, and in our everyday uses for it. Originally used for person-to-person (P2P) communication, i.e., Sally sends a text message to Betty – mobile messaging now offers tremendous value to businesses for customer and empl...
SYS-CON Events announced today that Sandy Carter, IBM General Manager Cloud Ecosystem and Developers, and a Social Business Evangelist, will keynote at the 17th International Cloud Expo®, which will take place on November 3–5, 2015, at the Santa Clara Convention Center in Santa Clara, CA.
The IoT market is on track to hit $7.1 trillion in 2020. The reality is that only a handful of companies are ready for this massive demand. There are a lot of barriers, paint points, traps, and hidden roadblocks. How can we deal with these issues and challenges? The paradigm has changed. Old-style ad-hoc trial-and-error ways will certainly lead you to the dead end. What is mandatory is an overarching and adaptive approach to effectively handle the rapid changes and exponential growth.
The IoT is upon us, but today’s databases, built on 30-year-old math, require multiple platforms to create a single solution. Data demands of the IoT require Big Data systems that can handle ingest, transactions and analytics concurrently adapting to varied situations as they occur, with speed at scale. In his session at @ThingsExpo, Chad Jones, chief strategy officer at Deep Information Sciences, will look differently at IoT data so enterprises can fully leverage their IoT potential. He’ll share tips on how to speed up business initiatives, harness Big Data and remain one step ahead by apply...
WebRTC converts the entire network into a ubiquitous communications cloud thereby connecting anytime, anywhere through any point. In his session at WebRTC Summit,, Mark Castleman, EIR at Bell Labs and Head of Future X Labs, will discuss how the transformational nature of communications is achieved through the democratizing force of WebRTC. WebRTC is doing for voice what HTML did for web content.
"Matrix is an ambitious open standard and implementation that's set up to break down the fragmentation problems that exist in IP messaging and VoIP communication," explained John Woolf, Technical Evangelist at Matrix, in this interview at @ThingsExpo, held Nov 4–6, 2014, at the Santa Clara Convention Center in Santa Clara, CA.
WebRTC has had a real tough three or four years, and so have those working with it. Only a few short years ago, the development world were excited about WebRTC and proclaiming how awesome it was. You might have played with the technology a couple of years ago, only to find the extra infrastructure requirements were painful to implement and poorly documented. This probably left a bitter taste in your mouth, especially when things went wrong.
Nowadays, a large number of sensors and devices are connected to the network. Leading-edge IoT technologies integrate various types of sensor data to create a new value for several business decision scenarios. The transparent cloud is a model of a new IoT emergence service platform. Many service providers store and access various types of sensor data in order to create and find out new business values by integrating such data.
The broad selection of hardware, the rapid evolution of operating systems and the time-to-market for mobile apps has been so rapid that new challenges for developers and engineers arise every day. Security, testing, hosting, and other metrics have to be considered through the process. In his session at Big Data Expo, Walter Maguire, Chief Field Technologist, HP Big Data Group, at Hewlett-Packard, will discuss the challenges faced by developers and a composite Big Data applications builder, focusing on how to help solve the problems that developers are continuously battling.
There are so many tools and techniques for data analytics that even for a data scientist the choices, possible systems, and even the types of data can be daunting. In his session at @ThingsExpo, Chris Harrold, Global CTO for Big Data Solutions for EMC Corporation, will show how to perform a simple, but meaningful analysis of social sentiment data using freely available tools that take only minutes to download and install. Participants will get the download information, scripts, and complete end-to-end walkthrough of the analysis from start to finish. Participants will also be given the pract...
WebRTC: together these advances have created a perfect storm of technologies that are disrupting and transforming classic communications models and ecosystems. In his session at WebRTC Summit, Cary Bran, VP of Innovation and New Ventures at Plantronics and PLT Labs, will provide an overview of this technological shift, including associated business and consumer communications impacts, and opportunities it may enable, complement or entirely transform.
SYS-CON Events announced today that Dyn, the worldwide leader in Internet Performance, will exhibit at SYS-CON's 17th International Cloud Expo®, which will take place on November 3-5, 2015, at the Santa Clara Convention Center in Santa Clara, CA. Dyn is a cloud-based Internet Performance company. Dyn helps companies monitor, control, and optimize online infrastructure for an exceptional end-user experience. Through a world-class network and unrivaled, objective intelligence into Internet conditions, Dyn ensures traffic gets delivered faster, safer, and more reliably than ever.